Semi-Abelian Schemes and Heights of Cycles in Moduli Spaces of Abelian Varieties
Semi-Abelian Schemes and Heights of Cycles in Moduli Spaces of Abelian Varieties
复制标题
阿贝尔簇模空间中的半阿贝尔格式和循环高度
DOI：
10.4171/rsmup/128-4
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
G. F. I. Montplet
中科院分区：
文献类型：
--
作者：
J. Bost;G. F. I. Montplet
我们研究了Barsotti-Tate群的可拓性质，并建立了算术变异上对数奇异厄米线束的涉及环高度的diophantine不等式。我们将这些结果应用于由Barsotti-Tate子群水平上的阿贝尔格式商所导出的阿贝尔变体模空间上函数域上数域上环的界高。为了达到这个目的，我们将我们的结果与可能开算术曲面上关于积分点的Rumely定理和等根类中关于阿贝尔格式高度的Faltings定理结合起来。
We study extension properties of Barsotti-Tate groups, and we establish diophantine inequalities involving heights of cycles with respect to logarithmically singular hermitian line bundles on arithmetic varieties. We apply these results to bound heights of cycles on moduli spaces of abelian varieties, induced by quotients of abelian schemes by levels of Barsotti-Tate subgroups, over function fields over number fields. To achieve this aim, we combine our results with Rumely’s theorem on integral points on possibly open arithmetic surfaces and with Faltings’ theorems on heights of abelian schemes in isogeny classes.